MS. HINEGARDNER
LESSON 1.1 EVALUATING EXPRESSIONS
ALGEBRAIC DEFINITION OF SUBTRACTION: (add-op)
a - b = a + -b ex) 5 - 2 = 5 + -2 = 3 4 - -10 = 4 + 10 = 14
ALGEBRAIC DEFINITION OF DIVISION:
a divided by b = a/b = a * 1/b
ASSOCIATIVE PROPERTY (addition and multiplication): move the groupings
(a + b) + c = a + (b + c)
(ab)c = a(bc) ex) (1.735 * 25) *4 = 1.735 * (25 * 4) = 173.5
TRANSITIVE PROPERTY
If a = b and b = c then a = c ex) if .5 = 50% and 50% = 1/2 then .5 = 1/2
PEMDAS- Order of operations
LESSON 1.2 PATTERNS
INSTANCE- Example *numbers*
PATTERN- general idea *variable*
instance
ex1) (5 + 8) + 10 = 5 + (8 + 10) ex2) 2 * 5 = 5 + 5
(2 + 7) + 9 = 2 + (7 + 9) 2 * 3 = 3 + 3
(4 + 2 ) + 6 = 4 + ( 2 + 6) 2 * .7 = .7 + .7
pattern
(x + y) + n = x + (y + n) 2 * a = a + a
pattern
ex3) wp = pw
instances
7*4 = 4*7
5*6 = 6*5
.8* 7 = 7*.8
COMMUTATIVE PROPERTY (addition and multiplication)
switch the order
LESSON 1.3 PATTERNS
sequence- a collection of numbers/objects in a specific order
terms- objects of the sequence
*if 2 expressions yield the same results they are equivalent
counterexample- an instance that proves the pattern is not true
LESSON 1.4 PICTURING EXPRESSIONS
scatterplot- graph with individual points not connected
connected graph use when there is a measure being graphed (length, time, area, or weight)
domain all the values that may be meaningfully substituted for the variable
set grouping numbers or objects {use the brackets}
roster {list}
set builder notation {x: x < 7}
| name of set (domain) | description | elements |
| whole numbers | {0, 1, 2, 3, ...} | 5, 16/2, 7 million, 0 |
| integers | {...-2, -1, 0, 1, 2 ...} whole #’s and their opposites (no parts/pcs) | -21/3, -17.00, 50 |
| real numbers | set of all numbers | 0, .3, -3.001, 4, ∏ |
| non-negative real numbers | pos set of numbers and 0 {x: x > 0} | 0, 3.2, 6000 |
LESSON 1.7 DATA AND SPREAD p47
range: largest - smallest
mu (mean) - add all the numbers together and divide by how many numbers there are
mean absolute deviation (m.a.d.)
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